Will bond yields in the United States hit a new all-time low in the wake of Brexit? It’s starting to look that way.

The yield on the U.S. 10-Year Treasury, a benchmark rate for many consumer and corporate loans, is currently at 1.45%.

It’s not to far off from the record low of 1.38% that the 10-Year Treasury hit in July 2012 when investors were worried that Spain may need a full-blown bailout.Several economists have recently said they wouldn’t be surprised if the 10-Year dips as low as 1% — especially since Federal Reserve chair Janet Yellen is now signaling that the Fed may be in no rush to raise interest rates again anytime soon.

But first, a little Fixed Income 101 reminder … bond yields and prices move in opposite directions. So the recent slide in rates means that investors have been buying a LOT of U.S. Treasuries lately.

That’s not necessarily the best of news for the markets — even if it’s good for borrowers. (If there’s one silver lining from Brexit, you might still have time to refinance your mortgage if you haven’t already … assuming you can find a bank willing to approve it.)

The strong appetite for U.S. bonds is a clear sign of how nervous investors are.

Even though CNNMoney’s Fear & Greed Index, which looks at seven measures of market sentiment, is currently in Neutral territory, the indicator for Safe Haven Demand (i.e. people flocking to bonds) is showing levels of Extreme Fear.

Clearly, Uncle Sam’s debt still seems attractive to other buyers despite the expected low rate of return — and also despite the fact that China and some other big foreign Treasury holders have been dumping U.S. government bonds in recent months.

And that makes sense. Even though a rate around 1.5% is obviously nothing to write home about, it’s higher than the yields of pretty much every other major economy.

France and The Netherlands have bond yields barely above zero while the 10-Year rates for Japan, Switzerland and Germany are in negative territory.

So what’s this all mean?

Investors have a bigger appetite for boring bonds than risky stocks. And it may “remain” that way for the foreseeable future. There’s no reason to “leave” bonds just yet.

“It may be too early to go bargain hunting,” wrote Ameriprise chief market strategist David Joy after the Brexit vote. “A defensive posture likely remains the best course of action until we have more clarity on the way forward, and that will take some time.”

Analysts at LPL Financial think investors will continue to flock to bonds as well. In a recent blog post, they wrote that U.S. Treasuries, while not cheap, “remain more attractively valued compared to their overseas counterparts in Germany and Japan.”

The LPL analysts added that there is still a debate about what’s fair value in this brave new world for the markets.

“Today’s bond valuations are expensive, but Treasuries remain among the best houses on a bad block,” they wrote.

In other words, investors may hold their nose and continue to buy U.S. bonds only because there aren’t many better places to park their cash.